Geometry Honors Summer Work Name: This packet is to be completed without a calculator. Please do all work directly on the page. Section 1: Simplifying and multiplying expressions Simplify each expression. 1. (5p2 – 3) + (2p2 – 3p3) 2. (a3 – 2a2) – (3a2 – 4a3) 3. (-‐4k4 + 14 + 3k2) + (-‐3k4 – 14k2 – 8) 4. (8n – 3n4 + 10n2) – (3n2 + 11n4 – 7) 5. (-‐5u3v4 + 9u) + (-‐5u3v4 – 8u + 8u2v2) + (-‐8u4v2 + 8u3v4) Find each product 6. 2x(-‐2x – 3) 7. -‐4(x + 1) 8. (2n + 2)(6n + 1) 9. (3m – 1)(8m + 7) 10. (x – 4)2 11. (x – 3)(x + 3) 12. (2k2 + 1)2 13. (3x + 7)(3x – 7) 14. (4a + 2)(6a2 – a + 2) 15. (6n2 – 6n – 5)(7n2 + 6n – 5)
Section 2: Factoring trinomials Factor each completely. 1. b2 + 8b + 7 2. n2 – 11n + 10 3. m2 + 2m – 24 4. x2 – 14x + 24 5. x2 – 25 6. 16n2 – 9 7. 100x2 + 180x + 81 8. 49n2 – 56n + 16 Section 3: Solving equations with one variable. You may also put no solutions or infinite solutions. ! ! 1. 4x = 20 2. 3 + x = -‐17 3. ! 𝑥 = 8 4. !! = 4 5. 2x – 8 = -‐32 6. 3x + 4x = -‐14 7. -‐36 = 6(2 – 8x) 8. –(-‐2x + 2) = -‐14 9. -‐6(x – 7) + 6(x + 5) = 73 10. 6x – 2x + 8 = x + 5 11. 4x + 5x + 15 = 5x + 7x 12. 2(x + 8) = -‐3(x + 3) 13. -‐5n – 4(-‐7 – 4n) = 36 + 7n
Section 4: Points, slope, graphing lines Plot each point
. Find the midpoint of the line segment with the given endpoints. 2. (-‐4, 4), (5, -‐1) 3. (2, -‐1), (-‐6, 0) 4. (3.1, -‐2.1), (-‐0.52, -‐0.6) Find the other endpoint of the line segment with the given endpoint and midpoint. 5. Endpoint: (-‐1, 9), midpoint: (-‐9, -‐10) Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary. 6. (5, 9), (-‐7, -‐7) 7. (8, 5), (-‐1, 3) Find the slope of the line through each pair of points. 8. (1, -‐19), (-‐2, -‐7) 9. (19, -‐2), (-‐11, 10) 10. (12, -‐18), (-‐15, -‐18)
Sketch the graph of each line. 11. x = 3
! 14. 𝑦 = ! 𝑥 − 2
12. y = -‐4
13. y = -‐6x + 3
!
15. 𝑦 = − ! 𝑥 + 3
16. 6x + 5y = 20
Section 5: Systems of equations (solving equations with two variables) Solve each system by elimination. 1. – 4x – 2y = -‐12 2. x – y = 11 3. -‐6x + 6y = 6 4x + 8y = -‐24 x + y = 19 -‐6x + 3y = -‐12 4. -‐4x + 9y = 9 5. 5x + 4y = -‐30 x – 3y = -‐6 3x – 9y = -‐18
Solve each system by Substitution 6. y = 2 7. y = 6x – 11 4x – 3y = 18 -‐2x – 3y = -‐7 Solve each system by graphing ! 9. 𝑦 = − ! 𝑥 + 3 10. y = -‐1 !
𝑦 = ! 𝑥 − 3
!
𝑦 = − ! 𝑥 + 4
8. -‐5x + y = -‐2 -‐3x + 6y = -‐12
11. y = -‐2x + 2
y = -‐2x – 2
Section 6: Square roots Simplify. Leave all answers in simplest radical form. 1. 216 2. 12 3. 10 96 5. −5 6 − 2 6 6. −3 24 − 3 2 + 2 2 7. 5 ∙ 5 8. 10 ∙ 2 9. 6 ∙ 2 9
4. 2 36
10. 4 3 ∙ 4 6